question_answer

Three identical particles are joined together by a thread as shown in figure.  All the three particles are moving in a horizontal plane.  If the velocity of the outermost particle is v0, then the ratio of tensions in the three sections of the string is                                    [UPSEAT 2003]

A)             3 : 5 : 7

B)                      3 : 4 : 5

C)             7 : 11 : 6

D)                      3 : 5 : 6

Correct Answer: D

Solution :

                Let \[\omega \] is the angular speed of revolution                         \[{{T}_{3}}=m{{\omega }^{2}}3l\]                         \[{{T}_{2}}-{{T}_{3}}=m{{\omega }^{2}}2l\] Þ \[{{T}_{2}}=m{{\omega }^{2}}5l\]                         \[{{T}_{1}}-{{T}_{2}}=m{{\omega }^{2}}l\Rightarrow {{T}_{1}}=m{{\omega }^{2}}6l\]             \[{{T}_{3}}:{{T}_{2}}:{{T}_{1}}=3:5:6\]